The key to understanding the behaviours of and for deriving solutions for the nematic DSW and its associated
resonant wavetrain will be a solution for the resonant wavetrain and a knowledge of its stability. To study this stability,
Whitham modulation theory will be used to generate modulation equations for the periodic wave solution of the nematic
equations [1]}. Unfortunately, there are no known general solitary wave or periodic wave solutions of the
nematic equations. However, the resonant wavetrain has small amplitude, so that the periodic wave solution will be found
as a Stokes' expansion, as was done for the Kahawara equation [2]} and the fifth order KdV equation, the Kahawara
equation (REF ) with \(\mu = 0\)  [3]}. We then seek a Stokes' expansion solution of the nematic equations as
\(\rho & = & \bar{\rho } + a \cos \varphi + a^{2} \rho _{2} \cos 2\varphi + a^{3} \rho _{3} \cos 3\varphi + \ldots ,  \\v & = & \bar{v} + av_{1}\cos \varphi + a^{2}v_{2} \cos 2\varphi + a^{3} v_{3} \cos 3\varphi + \ldots ,  \\\theta & = & \frac{\bar{\rho }}{q} + a\theta _{1} \cos \varphi + a^{2} \theta _{2} \cos 2\varphi + a^{3} \theta _{3} \cos 3\varphi + \ldots ,  \\\omega & = & \omega _{0} + a\omega _{1} + a^{2} \omega _{2} + \ldots , \) 
